Unfortunately I am not a finance expert and on my own...Currently I am struggling with the calculation of the instantaneous forward rate r in Hull-White: “Using Interest Rate Derivatives (p. 3).The equation should yield F(0,3)=0,078304 with P(0,3)= 0,827673348 and t=3 but how do you calculate this?!Thank you very much.

It is somewhat tedious, but not difficult. Take it step by step. First, rewrite the equations with t=0. You will see that simplifies things because P(0,t) becomes 1 and 1 - e^(1 - 2*a*t) becomes zero, wiping out the most complicated term. Then take the logarithm of P(0,T), then take the derivative with respect to T (I use capital T, because that's how the equations are written). You shouldn't have too much trouble.

Thank you for your help. Unfortunately I did not fully understand your suggestion. You are right that t=0 shortens the equations a lot but t won’t be 0 in the program I am trying to write based on the paper. Pls. could you explain even more detailed?

I thought you were trying to compute an analytic derivative, not write a program.What is the program going to do? Calibrate a Hull-White model from bond prices?

Hi Aaron, the program should calculate coupon bond options through Hull-White (trinomial) interest rate trees. I think I found a way around the differential in A C++ Encoded Hull-White Interest Rate Tree-Builder on page 7. At least I get the same results as stated in the original Hull-White paper from my posting underneath. I am about to implement the calculations in my program. The next problem will be to integrate the coupon in the calculations (that`s due for tonight). Are you familiar with the coupon calculation in trinomial trees? I just know that a coupon must be treated as an additional bond but I am not sure about the exact formulas / calculations required.Many thanks!

I doubt I'm the person here most familiar with them. I taught them and can do textbook problems, but I haven't worked with them professionally.